THE FLOW OF WATER IN CONCRETE PIPE. 45 



a low velocity in a large pipe is so small that it conflicts with the 

 ordinary errors of experimentation. 



For observation No. 1 (not included in Table 3) the water column 

 at gauge No. 2 was 0.017 foot higher than the column at gauge No 1 for 

 a velocity of 1.76 feet per second, whereas it should have been in the 

 neighborhood of 0.070 lower. There was absolutely no error in the 

 levels. Agreement between levels of the gauge glasses at the ends of 

 the reach as developed by the wye level and as shown by the static 

 pressure in the siphon with still water was within 0.001 foot. The 

 writer can account for the discrepancy between the actual gauge 

 heights (which indicated that there was a gain instead of a loss of 

 head) and the heights that might be expected only by explaining that 

 piezometer No. 1 is impinged upon by the water soon after pitching 

 downhill at the intake of the siphon, while piezometer No. 2 is sub- 

 jected to the current after the water has passed through 850 feet of 

 10-foot pipe, the last 200 feet of which are straight. 



The observations on this pipe listed in Table 3 were made at 

 velocities great enough so that a distinct loss of head was recorded, 

 but there is probably some of the same error that showed the gain 

 in head for observation No. 1. For this reason the writer does not 

 accord any weight to this series, but does not wish to suppress the 

 tests and uses them to emphasize the necessity of testing relatively 

 long reaches of pipe in order that the actual loss of head may far 

 overshadow the unavoidable experimental errors. 



For experience on pipes of larger sizes see Appendix. 



ANALYSIS OF THE EXPERIMENTAL DATA. 



Water flowing under pressure, confined on all sides, probably 

 follows a slightly different scheme as regards velocity distribution 

 from that of water which but partially fills the conduit, thus having a 

 surface exposed to the air. For this reason the results of experiments 

 under these two conditions will be discussed separately. 



FLOW IN PIPES UNDER PRESSURE. 



It has come to be generally understood that the relationship of 

 friction loss to velocity within a given pipe of any material can be 

 represented by the equation 



H = m V s (12) 



in which the values of z are as a rule between 1.70 and 2.00, although 

 there are many records of experiments in which the value of the 

 exponent z was in excess of 2. 



For a series of pipes of the same general characteristics but of 

 varying diameters the values of m follow the general equation 



m=Kd x (13) 



Substituting in formula 12 



H=Kd*V z (14) 



This expressed logarithmically becomes 



log H = log K+ x log d + z log V (15) 



